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Notes from good lectures

Vector bundles on curves

Notes from lectures by P. A. Vishwanath, L. Brambila-Paz, and W. Oxbury...
The notes in this section are pretty complete...

The following ones are not at all in final form...

Rationally connected varieties

Lectures by Joe Harris, Harvard
Notes by Joachim Kock
Trento, September 2001

1. Definition and good properties.
2. Consequences and extensions of the fibration theorem.
3. Some deformation theory.
4. Proof of the fibration theorem.
5. A converse of the fibration theorem.
6. Open problems.

20pp with nice figures. [ pdf ]

Special algebraic varieties

Lectures by Francesco Russo, UFPE, Recife
Notes by Joachim Kock
Recife, February 2000

1. Topology of algebraic varieties, connectedness theorems.
2. More about the Fulton-Hansen theorem.
3. Cohomological dimension, generalisation of Fulton-Hansen.
4. Complete intersections and Hartshorne's conjectures.
5. Second Hartshorne conjecture and the four Severi varieties.

16pp. [ ps ]

Nodal curves on surfaces

Lectures by Ciro Ciliberto, Rome
Notes by Joachim Kock
Recife, February 1999

1. Severi varieties.
2. Severi varieties of K3 surfaces.
3. Severi varieties of general surfaces.
4. Lower bounds for the genus of curves on general surfaces.

19pp with figures. [ ps ]

Last updated: 27th of October 2001 by Joachim Kock.